Z Score

The Z-Score is also popularly known as the Standard Score. This is a statistical value that tells us how many standard deviations away an element is from the computed mean.

The Z-Score value can be computed using the following formula:

Where Z is the value of the Z-Score

            X is the value of the element

            μ is the value of the mean

            σ is the value of the standard deviation

NOTE: The standard deviation σ is essentially the square root of the variance σ².

Case 1

The value of the Z-Score is zero.

When this happens we draw the conclusion that the value of the element and that of the mean are not different. This simply means that there are zero standard deviations between the value of random variable X used and the mean.

Case 2

The value of the Z-Score is positive.

When this happens we draw the conclusion that the value of the element is greater than that of the mean. A good example is a Z-Score value of +2. This is interpreted as the value of the element used being two standard deviations above that of the mean.

Case 3

The value of the Z-Score is negative.

When this happens we draw the conclusion that the value of the element is less than that of the mean. A good example is a Z-Score value of -2. This is interpreted as the value of the element used being two standard deviations below that of the mean.